s.t. sum_i w(i) = 1 sum_i r(i)w(i) >= R for_i w(i) - u(i) x(i) <= 0 i=1...n sum_i x(i) <= K for_i x(i) are binary i=1...n
where r(i) : return on asset i. u(i) : an upper bound on the proportion of total budget that could be invested on asset i. Q(i,j): covariance between the returns of i^th and j^th assets. K : max number of assets allowed in the portfolio w(i) : proportion of total budget invested on asset i x(i) : a 0-1 indicator if asset i is invested on.